I am too J brained so this is becoming a reblog instead of a comment because there is TOO MUCH to write because YES YES YES YES YOU GET IT SHE IS MY NUANCED MESS OF A GIRL
First, on her feelings about N because I think about this in so much detail every day: J hates N, but she doesn't want him to go. At the same time... she's jealous!
This has been a constant for a very long time. Ever since N gained some presence so pretty early within his introduction to the manor I reckon.
For one: The jealousy.
N is loveable, happy and willing to sacrifice himself for everyone. I truly do believe these are things that J envies, and at the same time she DESPISES and refuses to ever be like that herself.
It's foolish and careless in her eyes, but at the same time it means he is loved in such an unadulterated amount that she cannot help but feel her chest thighten about it. She knows that for better or worse she cannot do that for anyone else other than Tessa and herself. To a degree, she's too scared. She envies that boldness as someone who's SUPPOSED to be bold in her own eyes.
Not just that, but as someone who admires Tessa as much as she does (platonic or romantic interpretations do not change this in my opinion, J's need to be adored by Tessa is a crucial part of her days in the manor and in general, there is a reason WHY the Solver took Tessa and it's because of the way she impacted all of her drones), seeing N being so quickly adored by her because he DESERVES that love must be painful, really painful.
Sidenote: His widespread adoration extends to the Solver. She knows he's the favorite. He gets to live in bliss without memories while she's made to know EVERYTHING and live on with its torture.
In relation to that: Her hatred for him.
I truly think J hates him, or at the very minimun believes she does. (How strongly she ACTUALLY hates him VS how much of it is actually just deflection ONTO him is another matter altogether).
He's someone willing to throw himself into a firepit for anyone he loves and is always cheery and ready to have fun even in terrible situations. This is admirable, but it's also... it's a threat.
Again, even back in the manor J always had to be hyper-aware of her surroundings. Managing everything to keep both herself and Tessa safe. One mistake and a drone would end up scrapped and Tessa inevitably would end up abused for it (We do know her parents are abusive, although how much beyond what we see is unknown. It's bad, though.)
Someone that is so willing to find fun and sacrifice himself for others is also someone that is a DIRECT threat to that. He's unpredictable. Him covering for someone else could impact Tessa or get him scrapped (which eventually it does). This goes completely against everything that J has built to have a somewhat safe and stable life in a very volatile and abusive environment.
So of course, someone that dangerous must be despised. It's only reasonable. It's defensiveness, it's fear. Even if that's not the best of choices, people under trauma sometimes do whatever is necessary to survive and I know J is no different.
What's worse? She probably knows it's bad, but it just makes her hate him even MORE. Because it must be his fault! He's the reason her safety was disrupted! (Even though he's a victim too. It's easier. She can't fight her abusers, but she can fight him.)
Then on her latching onto him, but also V.
They are all she has of her past that is actually real. Even if she's delusionally latching onto the Solver's acts she still acts very aware that it is not Tessa. It may provide some comfort, but it also hurts.
V and N are themselves. They may have changed, but only as much as she has, they are still themselves.
If they stand out of line at BEST they will be reset and a new clone will be made, but at WORST? The Solver could get tired of them and decide that enough is enough and that's it for them.
Not just that, but either by the Solver's own doing or by J's past trauma she may even fear that them standing out of line will end up hurting her, too. I do not think there's one singular "thing" but more of a combination of issues causing her to latch on.
She is... ultimately not a lonely person. She's always depended on having someone else by her side. She may be bossy— which I think is a trait she had from the beginning but got intensified into a coping mechanism over time— but she just does not do well being alone, or even being the one stuck managing everything.
Managing stuff is stressful, it's scary! One wrong step and it's all over. Having someone telling her what to do removes some level of that responsability, she's never truly put herself at the top, just in a role that is in the middle.
Buut to have that role in the middle, she has to have someone to latch onto. Someone that she can boss around, but also someone that she feels is close enough to her that she can be not-alone.
Similarly, I also just think J cannot survive by herself. Even if she were perfectly capable, she'd crumble.
She needs to be surrounded by others to survive even if it's by force. She does not care how much she has to hurt them, she knows she cannot live if she's alone.
She needs them, she KNOWS she needs them, she has to keep them submissive enough so she won't be left behind. She cannot handle the idea that she's being abandoned, even if she thinks she hates them beyond belief.
It's unhealthy— unsure if she knows this or not— and she will do anything to make sure they are her stable constant through hell because she knows there is no way out.
Then on her not thinking defeating Cyn was possible! Because I truly do think this is an absolute for her.
The Solver has made it VERY well known for her that there is no way out. Rebelling won't lead to death (an "end", even though I think J is genuinely too afraid to die to give in if death was an option), it will just lead to being hurt and forced until there is no other paths to take.
As long as you are useful, you don't get a choice. Trying to escape will just lead to being hurt. J has NEVER had another point of reference.
Before the Solver it was the manor, and we know how that went.
J is a chronically afraid person (er, drone, whichever). She's basically like those experiments where if a rat gets shocked enough, it will stop doing whatever it relates to the shock.
Rebelling leads to pain and never gets a success, thereby rebelling must be useless!
Seeing them leave was the ultimate betrayal. Not only did she believe they were wrong and that she could lose them from it, but also because once it became evident that she was wrong she really felt it was too late (those shackles are on TIGHT man) and she was shamefully "banished" (by her own choice) because she cannot see a world where they would let her in. Why would they?